The probability that you will buy a certain product or adopt a certain opinion, lies at the heart of one of the hottest problems in network theory: how to predict whether a product, opinion or message is likely to go viral.

There is no shortage of potential answers. Indeed, one of the important successes of network theory is that it demonstrates how information spreads through a network based on the connectivity of the individuals within it.

And yet marketers have yet to exploit this idea in a way that produces reliable and repeatable results. The truth is that marketing is as much of a black art as ever.

That could soon change thanks to the work of Xiao Fang and pals at the University of Utah in Salt Lake City. Today, these guys unveil a technique that predicts the adoption probability of individuals within a network and say it dramatically outperforms previous efforts.

They say their new technique will allow marketers to target their campaigns more effectively and to fine tune messages for the individual customers most likely to adopt a new service at that specific moment.

First, some background. The standard method for simulating the way information spreads through a network is known as the cascade model. This assumes that a person will receive a piece of information if a certain number of his or her nearest neighbours also have it. In other words, the adoption probability is a social effect that depends on the influence of friends, family and other close associates.

This approach has had much success in modelling the spread of disease, fashions, viral emails and so on. But network scientists know that it is far from perfect.

The problem is that there are many other effects that also influence whether or not an individual adopts an idea or buys a product. For example, an individual may become more likely to buy a product because of marketing efforts that target him or her offline. Things like maildrops, billboards, TV adverts and so on.

In fact, these so-called confounding effects are so powerful that they defy network theorists’ attempts to model the behaviour of real individuals on real networks.

The problem in modelling the effect of real marketing efforts is that their success rate is usually so low that it can appear negligible in a cascade model. For example, imagine that a company sends information about a new product to all its existing companies. The truth is that if half a percent of all these customers take up the offer, marketers would consider this a huge success.

But in a cascade model, if half a percent of an individual’s friends buy a new product, that’s essentially none of them. So this model predicts that nobody will buy the product. It simply cannot handle the small but significant level at which much marketing goes on.

That’s where the work of Xiao Fang and co comes in. These guys have created a network model that takes confounding effects into account when assessing how likely it is that a particular individual will adopt an idea or buy a product. It specifically allows for the slight bias that offline influences, like advertising campaigns, may have.

And Xiao Fang and co say it works too. These guys have tested their new approach on a database of 35,000 mobile phone customers who were able to choose between 18 different payment plans.

The database shows how many customers adopted a new plan each day over the course of a year. This occurred at the modest rate of about 0.4 per cent.

This rate may be a result of social network effects such as friends recommending the same plan to each other. But it may also be the result of the companies own marketing efforts, which are not recorded on the network.

The task for Xiao Fang and co is to model how customers adopted to the new payment plan in question. They found that conventional cascade models essentially fail to predict any significant take up at all.

However, their new approach was significantly more successful. They say the ability to account for unknown confounding effects allows them to model that actual take up rate successfully, even though it was only 0.4 per cent.

What’s more their model shows which nodes in a network are most likely to be tipped by offline effects. That’s important because it allows marketers to target their campaigns much more effectively and to monitor their success in real time.

Indeed, the new approach raises the prospect of creating personalised messages aimed at specific individuals at exactly the moment when they are most vulnerable. “Firms can become more effective in seed selection for viral marketing and perform the selection dynamically over time,” they say.

Of course, it’s one thing to successfully predict the evolution of historical data. Its quite another to predict the future evolution of current data. That will be the real test of this new idea. And if it succeeds, Xiao Fang and co will have the viral marketing world beating a path to their door.